한국수학교육학회지시리즈E:수학교육논문집 (Communications of Mathematical Education)

  • 제37권3호
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  • Pages.419-442
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  • 2023
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  • 1226-6663(pISSN)
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  • 2287-9935(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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초등학교 5학년 학생들의 일반화된 산술 관점과 함수적 관점에서의 변수에 대한 이해

Fifth Graders' Understanding of Variables from a Generalized Arithmetic and a Functional Perspectives

  • Pang, JeongSuk (Korea National University of Education) ;
  • Kim, Leena (Graduate School of Korea National University of Education) ;
  • Gwak, EunAe (Seongnam jeil elementary school)
  • 투고 : 2023.08.21
  • 심사 : 2023.09.23
  • 발행 : 2023.09.30
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초록

본 연구는 초기 대수의 일반화된 산술 관점과 함수적 관점에서 초등학교 5학년 학생들의 변수에 대한 이해 실태를 조사하였다. 구체적으로 전자에서는 1의 성질, 덧셈의 교환법칙, 곱셈의 결합법칙, 산술 맥락에서의 문제 상황을 포함하였고, 후자에서는 덧셈 관계, 곱셈 관계, 제곱 관계, 선형 관계를 다루었다. 11개 학교에서 246명의 학생들을 대상으로 조사한 결과, 학생들은 공통적으로 변수에 해당하는 특정한 값을 구할 수 있었고, 변수를 활용한 식에서 다른 기호를 사용하여 식을 바꿔 쓸 수도 있다는 점을 이해하는 것으로 드러났다. 그러나 정해지지 않은 양을 포함한 산술 맥락에서의 문제 상황을 변수를 활용하여 일반화된 식으로 나타내는 데 많은 어려움을 겪었다. 또한 1의 성질과 덧셈의 교환법칙을 나타낸 식에서 변수는 자연수만 된다고 생각하는 경향이 있었으며, 약 25%의 학생들은 변수가 한 가지 수로 정해져 있다고 생각하였다. 이와 같은 연구 결과를 바탕으로 본 논문은 초등학생들의 변수 이해 및 지도에 대한 시사점을 제시하였다.

This study investigated fifth graders' understanding of variables from a generalized arithmetic and a functional perspectives of early algebra. Specifically, regarding a generalized perspective, we included the property of 1, the commutative property of addition, the associative property of multiplication, and a problem context with indeterminate quantities. Regarding the functional perspective, we covered additive, multiplicative, squaring, and linear relationships. A total of 246 students from 11 schools participated in this study. The results showed that most students could find specific values for variables and understood that equations involving variables could be rewritten using different symbols. However, they struggled to generalize problem situations involving indeterminate quantities to equations with variables. They also tended to think that variables used in representing the property of 1 and the commutative property of addition could only be natural numbers, and about 25% of the students thought that variables were fixed to a single number. Based on these findings, this paper suggests implications for elementary school students' understanding and teaching of variables.

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